The coherence of convex roof \(C_{c}\)  is a coherence measure [1]}, [2]}, [3]}, [4]}. According to
the coherence measure \(C_{c}\) , all maximally coherent states in an \(n\) -dimensional system can be transformed into the pure states in the following set by unitary incoherent operations [5]}:
\(\lbrace \frac{1}{\sqrt{n}} \sum _{j=0}^{n-1} e^{{\rm i}\theta _j} |j\rangle \ |\ \theta _1, \cdots , \theta _{n-1}\in [0,\ 2\pi )\rbrace .\) 
